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arXiv · 2607.02104

When Can You Debias an LLM Judge? Identifiability Limits, a Test, and Designs for Top-k Ranking

Jian Xu·Delu Zeng·John Paisley·Qibin Zhao
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Abstract

Large language models (LLMs) are increasingly used as cheap, scalable judges that compare candidate outputs pairwise. Because such judges prefer verbose or well-formatted answers, the natural fix is to add bias covariates to a Bradley--Terry model and estimate the bias away. We show this cannot work as advertised: the quality/bias split is \emph{not identified} by pairwise comparisons, and the failure is exact -- across $48$ real judge-pools the profile likelihood over the coefficient is flat to $\mathbf{0.0000}$ \textbf{nats}, and scaling the comparisons $26\times$ buys none. A ``debiased'' score is selected by the prior, not recovered from data. Our contribution is accordingly not a better estimator but a characterization of \emph{when prior-based correction is justified}, plus designs that supply the missing information when it is not. The assumption the prior encodes -- quality is a priori uncorrelated with the covariate -- pays only while $\mathrm{corr}(θ,x)$ stays below a crossing point (configuration-dependent, $0.22$--$0.60$), which is what makes the same model help on LLMBar and hurt on SummEval and Nectar. We give two escapes: a \textbf{trusted-anchor gate} that decides per (judge, covariate, task) (no false enables in $6{,}000$ decisions at $K\ge10$ anchors, a rate our sample bounds at $\le6\%$), and a \textbf{paired rendering design}. Across fifteen real LLM judges bias is heterogeneous and capability-dependent: correction improves \topk{} recall by $0.20$--$0.32$ on five biased-but-competent cheap judges and is a no-op on frontier ones (Spearman $ρ{=}{-}0.84$ between competence and gain over the $14$ competent judges, $p{<}10^{-3}$), concentrating the benefit where at-scale evaluation happens.

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Jian Xu, Delu Zeng, John Paisley, Qibin Zhao. 2026-07-18. When Can You Debias an LLM Judge? Identifiability Limits, a Test, and Designs for Top-k Ranking. https://arxiv.org/abs/2607.02104

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